The present invention relates to methods for determining fluid flow properties of porous media by using nuclear magnetic resonance (NMR) in combination with magnetic field gradients to encode fluid molecule displacements. Examples of fluid flow properties include but are not limited to the measurement of the effective porosity, pore connectivity, distribution of flow velocities, and tortuosity of porous media such as naturally occuring rocks. In particular the present invention relates to measuring the fluid flow transport properties by nuclear magnetic resonance (NMR) using magnetic field gradients to encode the distribution of fluid flow velocities and to encode the spatial distribution of fluid flow in a porous material while a steady fluid pressure gradient is applied.
Nuclear magnetic resonance has been used for some time to study fluid flow [A. Caprihan and E. Fukushima, Physics Reports, 198, 195 (1990)]. In general fluid flow can be quantified with NMR by using switched magnetic field gradients. With the application of a magnetic field gradient the precession frequency of a magnetic moment (in this case the nuclear magnetic moment) is a function of position coordinate z in the direction of the applied field gradient: EQU .omega.=.gamma.(H.sub.o +G.multidot.r) (1)
There exist several different classes of NMR experiments which quantitate flow: time-of-flight methods and phase encoding methods. For the heterogeneous media the phase encoding method is preferable, although the present invention does in principle work with both techniques. In the time of flight method spins in a slice of thickness and orientation determined by the applied gradient are prepared in a well defined state using rf pulses. After letting a time .DELTA. elapse the distribution of transverse magnetization is imaged and from the observed displacements and time .DELTA. one can calculate a velocity distribution spectrum. Time-of-flight techniques for measuring fluid flow are well established in medical application of magnetic resonance imaging (MRI) for MRI angiography.
In a phase encoding experiment the position of each fluid spin is tagged with a gradient pulse of duration .delta.. After letting a time .DELTA. elapse a gradient pulse of opposite polarity is applied. For stationary spins the phase acquired during the first gradient pulse is reversed by the second pulse which should be matched in duration and amplitude. For moving spins the phase reversal is incomplete depending on the displacement distance between the two gradient pulses. By repeating the experiment and systematically incrementing the amplitude of the matched gradient pulses one obtains a 2-d array of NMR signals as in an NMR imaging experiment. A Fourier transform of the data set of signals acquired with evenly incremented motion encoding gradient pulses will provide a spectrum of the distribution of fluid molecule displacements. There are numerous implementations of this measurement method. For porous media with low fluid flow permeability the stimulated echo sequence is most convenient for encoding slow flow as the duration .DELTA. between gradient pulses is limited by the longitudinal relaxation time T.sub.1, which is generally longer than the transverse relaxation time T.sub.2. Furthermore this NMR pulse sequence is more suitable to the application of techniques for cancelation of constant magnetic background gradients, characteristic of heterogeneous systems such as porous media when they are placed in a magnetic field.
The present invention provides a method for obtaining at least one fluid transport properties of a porous material under steady flow conditions and encoding the fluid motion from the nuclear magnetic resonance (NMR) signal of the fluid molecules.
In one embodiment of the present invention, a flow velocity distribution spectrum is obtained, which shows the fraction of spins moving at a certain velocity through the pore space. From this the ratio of moving spins to stationary spins can be calculated and this ratio provides a measure of the effective porosity. The total porosity of a porous material is defined as the volume ratio of void space and grain space. For flow through porous media the pore space connectivity determines what fraction of fluid filling the pore space is movable. Fluid in isolated and dead ended pores does not move when an external pressure gradient is applied. Total porosity encompasses both the contribution from interconnected and isolated pores. Effective porosity measures the volume fraction of the interconnected part of pore space from which fluids can be recovered by application of pressure gradients. This parameter is of importance in oil reservoir modeling and the methods used to date for determination of the effective porosity involved time-consuming nuclear tracer techniques.